a double sum of

USAGE SUMMARY

The phrase "a double sum of" is correct and usable in written English.
It can be used in mathematical or statistical contexts to refer to the summation of two separate sums. Example: "The total cost can be calculated as a double sum of the fixed and variable expenses."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

1 human-written examples

The minimisation following (9) is an optimisation problem of the least squares type featuring a double sum of experiments e = 1,…, E and time points k = 1,…, T e, i.

BMC Systems Biology

Human-verified similar examples from authoritative sources

Similar Expressions

59 human-written examples

One may be interested in a quicker but approximate computation by only taking the double sum of the earthquake pairs closer than a certain distance, such as 4 times of the Utsu Spatial Distance 3.33 × 100.5M−2 km (cf., Section 3).

Earth, Planets and Space

Each term of the double sum of Eq. 10 corresponds to a different degree n k, where n k is a real number.

Earth, Planets and Space

Reversing the double sum of (A.11) and using [10, equation (8.352.4 ], we obtain (A.2).

EURASIP Journal on Wireless Communications and Networking

The first is an implementation of Implicit SGD (ISGD), a stable but difficult to implement SGD method, and the second is a new SGD method specifically designed for optimizing a double-sum formulation of the softmax.

Columbia University

This triangular double integral is defined by single limit of double sums of triangularly divided areas.

Advances in Difference Equations

The antisymmetric double integral here introduced demands only single limit of double sums of triangularly divided areas.

Advances in Difference Equations

Dividing these pieces of plane by upper-right part and lower-left one, we may express them as the two kinds of double sums of areas.

Advances in Difference Equations

4. In the case of n → ∞, i.e., for a segment of A B ¯ and a piecewise smooth curve of equation f x, y) = 0, as shown in Figure 4, the area σ surrounded by the segment and the curve is σ = 1 2 lim n → ∞ ∑ k = 1 n ∑ j = 1 k Δ x k Δ y j - Δ y k Δ x j. (2.25)   Figure 4 Single limit at infinity n → ∞ of double sums of triangularly divided areas.

Advances in Difference Equations

In the paper, the authors establish several closed expressions for the Euler numbers in the form of a determinant or double sums and in terms of, for example, the Stirling numbers of the second kind.

Journal of Inequalities and Applications

In this paper, the effect of several axisymmetric elastic singularities (i.e., point forces, double forces, sum of two double forces and centers of dilatation) on the elastic response of a multilayered solid is investigated.

International Journal of Solids and Structures

Expert writing Tips

Best practice

When using "a double sum of", ensure that the context clearly indicates what quantities are being summed in each stage of the double summation. Provide relevant labels or indices to enhance understanding.

Common error

Avoid using "a double sum of" without clearly defining the indices and limits of each summation. Ambiguity in the indices can lead to misinterpretations of the mathematical expression. Always specify the range and variable being summed over.

Linguistic Context

The phrase "a double sum of" functions primarily as a descriptive term in mathematical and statistical contexts. It signifies that a summation process is applied twice, often involving nested summations over two or more indices or variables. Ludwig AI confirms its usability in English.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

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Ludwig's WRAP-UP

The phrase "a double sum of" is a mathematically descriptive term indicating a two-stage summation process, as confirmed by Ludwig AI. It's grammatically correct and predominantly used within scientific and academic contexts to define complex calculations. While not frequently encountered, understanding its proper usage is essential for clarity in technical writing. Remember to clearly define the summation indices to avoid ambiguity. Alternative phrases, like "the sum of two sums", can offer stylistic variations while maintaining precision.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

the sum of two sums

Focuses on the act of summing two separate sums, emphasizing the individual sums being combined.

the total of two summations

Replaces 'sum' with 'summation' for a more formal tone, suitable for mathematical contexts.

a summation of two terms

Highlights the individual components being added together in a broader summation process.

the aggregate of dual summations

Uses 'aggregate' for a more general summation concept and 'dual' to explicitly state the double nature.

a cumulative total from both sums

Implies the result of adding two sums and accumulating the total.

the combined sum

Emphasizes the result of adding multiple quantities in one combined value.

the total from summing twice

Explicitly states that the summation process occurs in two stages.

the grand total of summations

Conveys the final result after all summations have been performed, suggesting a complete accumulation.

an accumulated sum

Focuses on the progressive nature of the summation, resulting in an accumulated total.

a composite summation

Indicates that the summation comprises several sub-summations, producing a final composite result.

FAQs

How is "a double sum of" used in mathematical contexts?

In mathematics, "a double sum of" refers to the summation of a sum, typically involving two indices. For example, it can represent the sum of rows and columns in a matrix or the calculation of a double integral by discretizing the area.

What are some alternatives to "a double sum of" in scientific writing?

Alternatives to "a double sum of" include "the sum of two sums", "the total of two summations", or "a summation of two terms", depending on the desired level of formality and precision.

Is "a double sum of" grammatically correct?

Yes, "a double sum of" is grammatically correct. Ludwig AI confirms that it is usable in written English, particularly in technical or mathematical contexts.

In what contexts can I use "a double sum of"?

"A double sum of" is typically used in mathematical, scientific, or engineering contexts where it is necessary to express the cumulative result of two levels of summation, such as in statistical analysis or physics calculations. Always ensure that your audience understands the specific mathematical meaning.